Extensions of the classical finite operator calculus of Rota–Mullin are presented. Extended calculi are examples of algebraization of the difference and/or differential analysis of linear operators acting on polynomials. Such analysis becomes equivalent to the use of properties of Graves–Heisenberg–Weyl algebra. The skew product form of the algebra End(F[x]) of operators on the linear space F[x] of polynomials plays implicitly a crucial role due to Maximov's expansion theorem recently proved in its general form. The aim of this communication is to list a sequence of main extended umbral theorems in a simple structure regime. The proofs if not easy are given elsewhere and are referred to.